Octahedron reference axis

These two ligating atoms, the priority 1 atom and the (lowest priority) atom trans to it, define the reference axis of the octahedron. 

Figure 3.27 The relationship between the cube and (a) the tetrahedron and (b) the octahedron. The axis system shown can be used as a common reference frame for all three figures.

Figure 5.21 The d-orbital energy levels for the central atom of an Oh complex the diagram to the right shows the reference axis system for the octahedron.

Figure 21 The La2Cu04 structure, a) Structure showing distorted octahedron and puckered CuOz planes, b) Illustration of the tilted octahedra (0 = 4.5°), and rotation about the b axis = 1°). From Reference 108.

Fig. 22 Temperature dependence of magnetic functions (level-6) for different axial crystal-field strength F4(z) of Ti(III) complexes. From left to right Fnixy) = 4000, 8000, 13000, and 18000 cnr1. Black lines refer to the regular octahedron. Note temperature axis runs oppositely between the top and bottom panels...

Figure 10 The effect of particle size on the change in the normalized Pt J-band vacancies d-band vacancies/% surface atoms) (...) in going from 0.54 to 0.0 V. The change in the Pt-Pt coordination number as determined from the Pt L3 edge EXAFS analysis is also shown (—). The ordinate axis refers to the change in the J-band vacancy/atom determined from XANES spectra normalized with respect to total number of surface atoms present (based on cluster calculations on a cubo-octahedron model). 

The regular octahedron can be used to describe the three-fold inversion axis, 3, (pronounced three bar ). As with the regular tetrahedron, it is convenient to refer to Cartesian axes to locate the symmetry operators, (Figure 4.7a). The highest order axis, however, is not 3, but a tetrad. These axes pass through a vertex and run along the jc-, y- and z-axes. Each tetrad is accompanied by a mirror normal to it, (Figure 4.7b). This combination is written 4/m (pronounced 4 over em ). 

The symmetry elements for Ot, were discussed in Section 3.9. To set up the reference frame for the complex it is usual to align the axis system with the metal ligand bonds so that the ligands can be thought of as lying at the corners of the standard octahedral shape. This arrangement is also used in the three-dimensional model from Appendix 4, which also has the same set of example symmetry elements drawn on the paper octahedron. 

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